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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.optimization.univariate;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.util.Precision;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.optimization.ConvergenceChecker;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.optimization.GoalType;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * For a function defined on some interval {@code (lo, hi)}, this class<a name="line.27"></a>
<FONT color="green">028</FONT>     * finds an approximation {@code x} to the point at which the function<a name="line.28"></a>
<FONT color="green">029</FONT>     * attains its minimum.<a name="line.29"></a>
<FONT color="green">030</FONT>     * It implements Richard Brent's algorithm (from his book "Algorithms for<a name="line.30"></a>
<FONT color="green">031</FONT>     * Minimization without Derivatives", p. 79) for finding minima of real<a name="line.31"></a>
<FONT color="green">032</FONT>     * univariate functions.<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;br/&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * This code is an adaptation, partly based on the Python code from SciPy<a name="line.34"></a>
<FONT color="green">035</FONT>     * (module "optimize.py" v0.5); the original algorithm is also modified<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;ul&gt;<a name="line.36"></a>
<FONT color="green">037</FONT>     *  &lt;li&gt;to use an initial guess provided by the user,&lt;/li&gt;<a name="line.37"></a>
<FONT color="green">038</FONT>     *  &lt;li&gt;to ensure that the best point encountered is the one returned.&lt;/li&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     * &lt;/ul&gt;<a name="line.39"></a>
<FONT color="green">040</FONT>     *<a name="line.40"></a>
<FONT color="green">041</FONT>     * @version $Id: BrentOptimizer.java 1422230 2012-12-15 12:11:13Z erans $<a name="line.41"></a>
<FONT color="green">042</FONT>     * @deprecated As of 3.1 (to be removed in 4.0).<a name="line.42"></a>
<FONT color="green">043</FONT>     * @since 2.0<a name="line.43"></a>
<FONT color="green">044</FONT>     */<a name="line.44"></a>
<FONT color="green">045</FONT>    @Deprecated<a name="line.45"></a>
<FONT color="green">046</FONT>    public class BrentOptimizer extends BaseAbstractUnivariateOptimizer {<a name="line.46"></a>
<FONT color="green">047</FONT>        /**<a name="line.47"></a>
<FONT color="green">048</FONT>         * Golden section.<a name="line.48"></a>
<FONT color="green">049</FONT>         */<a name="line.49"></a>
<FONT color="green">050</FONT>        private static final double GOLDEN_SECTION = 0.5 * (3 - FastMath.sqrt(5));<a name="line.50"></a>
<FONT color="green">051</FONT>        /**<a name="line.51"></a>
<FONT color="green">052</FONT>         * Minimum relative tolerance.<a name="line.52"></a>
<FONT color="green">053</FONT>         */<a name="line.53"></a>
<FONT color="green">054</FONT>        private static final double MIN_RELATIVE_TOLERANCE = 2 * FastMath.ulp(1d);<a name="line.54"></a>
<FONT color="green">055</FONT>        /**<a name="line.55"></a>
<FONT color="green">056</FONT>         * Relative threshold.<a name="line.56"></a>
<FONT color="green">057</FONT>         */<a name="line.57"></a>
<FONT color="green">058</FONT>        private final double relativeThreshold;<a name="line.58"></a>
<FONT color="green">059</FONT>        /**<a name="line.59"></a>
<FONT color="green">060</FONT>         * Absolute threshold.<a name="line.60"></a>
<FONT color="green">061</FONT>         */<a name="line.61"></a>
<FONT color="green">062</FONT>        private final double absoluteThreshold;<a name="line.62"></a>
<FONT color="green">063</FONT>    <a name="line.63"></a>
<FONT color="green">064</FONT>        /**<a name="line.64"></a>
<FONT color="green">065</FONT>         * The arguments are used implement the original stopping criterion<a name="line.65"></a>
<FONT color="green">066</FONT>         * of Brent's algorithm.<a name="line.66"></a>
<FONT color="green">067</FONT>         * {@code abs} and {@code rel} define a tolerance<a name="line.67"></a>
<FONT color="green">068</FONT>         * {@code tol = rel |x| + abs}. {@code rel} should be no smaller than<a name="line.68"></a>
<FONT color="green">069</FONT>         * &lt;em&gt;2 macheps&lt;/em&gt; and preferably not much less than &lt;em&gt;sqrt(macheps)&lt;/em&gt;,<a name="line.69"></a>
<FONT color="green">070</FONT>         * where &lt;em&gt;macheps&lt;/em&gt; is the relative machine precision. {@code abs} must<a name="line.70"></a>
<FONT color="green">071</FONT>         * be positive.<a name="line.71"></a>
<FONT color="green">072</FONT>         *<a name="line.72"></a>
<FONT color="green">073</FONT>         * @param rel Relative threshold.<a name="line.73"></a>
<FONT color="green">074</FONT>         * @param abs Absolute threshold.<a name="line.74"></a>
<FONT color="green">075</FONT>         * @param checker Additional, user-defined, convergence checking<a name="line.75"></a>
<FONT color="green">076</FONT>         * procedure.<a name="line.76"></a>
<FONT color="green">077</FONT>         * @throws NotStrictlyPositiveException if {@code abs &lt;= 0}.<a name="line.77"></a>
<FONT color="green">078</FONT>         * @throws NumberIsTooSmallException if {@code rel &lt; 2 * Math.ulp(1d)}.<a name="line.78"></a>
<FONT color="green">079</FONT>         */<a name="line.79"></a>
<FONT color="green">080</FONT>        public BrentOptimizer(double rel,<a name="line.80"></a>
<FONT color="green">081</FONT>                              double abs,<a name="line.81"></a>
<FONT color="green">082</FONT>                              ConvergenceChecker&lt;UnivariatePointValuePair&gt; checker) {<a name="line.82"></a>
<FONT color="green">083</FONT>            super(checker);<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>            if (rel &lt; MIN_RELATIVE_TOLERANCE) {<a name="line.85"></a>
<FONT color="green">086</FONT>                throw new NumberIsTooSmallException(rel, MIN_RELATIVE_TOLERANCE, true);<a name="line.86"></a>
<FONT color="green">087</FONT>            }<a name="line.87"></a>
<FONT color="green">088</FONT>            if (abs &lt;= 0) {<a name="line.88"></a>
<FONT color="green">089</FONT>                throw new NotStrictlyPositiveException(abs);<a name="line.89"></a>
<FONT color="green">090</FONT>            }<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>            relativeThreshold = rel;<a name="line.92"></a>
<FONT color="green">093</FONT>            absoluteThreshold = abs;<a name="line.93"></a>
<FONT color="green">094</FONT>        }<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>        /**<a name="line.96"></a>
<FONT color="green">097</FONT>         * The arguments are used for implementing the original stopping criterion<a name="line.97"></a>
<FONT color="green">098</FONT>         * of Brent's algorithm.<a name="line.98"></a>
<FONT color="green">099</FONT>         * {@code abs} and {@code rel} define a tolerance<a name="line.99"></a>
<FONT color="green">100</FONT>         * {@code tol = rel |x| + abs}. {@code rel} should be no smaller than<a name="line.100"></a>
<FONT color="green">101</FONT>         * &lt;em&gt;2 macheps&lt;/em&gt; and preferably not much less than &lt;em&gt;sqrt(macheps)&lt;/em&gt;,<a name="line.101"></a>
<FONT color="green">102</FONT>         * where &lt;em&gt;macheps&lt;/em&gt; is the relative machine precision. {@code abs} must<a name="line.102"></a>
<FONT color="green">103</FONT>         * be positive.<a name="line.103"></a>
<FONT color="green">104</FONT>         *<a name="line.104"></a>
<FONT color="green">105</FONT>         * @param rel Relative threshold.<a name="line.105"></a>
<FONT color="green">106</FONT>         * @param abs Absolute threshold.<a name="line.106"></a>
<FONT color="green">107</FONT>         * @throws NotStrictlyPositiveException if {@code abs &lt;= 0}.<a name="line.107"></a>
<FONT color="green">108</FONT>         * @throws NumberIsTooSmallException if {@code rel &lt; 2 * Math.ulp(1d)}.<a name="line.108"></a>
<FONT color="green">109</FONT>         */<a name="line.109"></a>
<FONT color="green">110</FONT>        public BrentOptimizer(double rel,<a name="line.110"></a>
<FONT color="green">111</FONT>                              double abs) {<a name="line.111"></a>
<FONT color="green">112</FONT>            this(rel, abs, null);<a name="line.112"></a>
<FONT color="green">113</FONT>        }<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>        /** {@inheritDoc} */<a name="line.115"></a>
<FONT color="green">116</FONT>        @Override<a name="line.116"></a>
<FONT color="green">117</FONT>        protected UnivariatePointValuePair doOptimize() {<a name="line.117"></a>
<FONT color="green">118</FONT>            final boolean isMinim = getGoalType() == GoalType.MINIMIZE;<a name="line.118"></a>
<FONT color="green">119</FONT>            final double lo = getMin();<a name="line.119"></a>
<FONT color="green">120</FONT>            final double mid = getStartValue();<a name="line.120"></a>
<FONT color="green">121</FONT>            final double hi = getMax();<a name="line.121"></a>
<FONT color="green">122</FONT>    <a name="line.122"></a>
<FONT color="green">123</FONT>            // Optional additional convergence criteria.<a name="line.123"></a>
<FONT color="green">124</FONT>            final ConvergenceChecker&lt;UnivariatePointValuePair&gt; checker<a name="line.124"></a>
<FONT color="green">125</FONT>                = getConvergenceChecker();<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>            double a;<a name="line.127"></a>
<FONT color="green">128</FONT>            double b;<a name="line.128"></a>
<FONT color="green">129</FONT>            if (lo &lt; hi) {<a name="line.129"></a>
<FONT color="green">130</FONT>                a = lo;<a name="line.130"></a>
<FONT color="green">131</FONT>                b = hi;<a name="line.131"></a>
<FONT color="green">132</FONT>            } else {<a name="line.132"></a>
<FONT color="green">133</FONT>                a = hi;<a name="line.133"></a>
<FONT color="green">134</FONT>                b = lo;<a name="line.134"></a>
<FONT color="green">135</FONT>            }<a name="line.135"></a>
<FONT color="green">136</FONT>    <a name="line.136"></a>
<FONT color="green">137</FONT>            double x = mid;<a name="line.137"></a>
<FONT color="green">138</FONT>            double v = x;<a name="line.138"></a>
<FONT color="green">139</FONT>            double w = x;<a name="line.139"></a>
<FONT color="green">140</FONT>            double d = 0;<a name="line.140"></a>
<FONT color="green">141</FONT>            double e = 0;<a name="line.141"></a>
<FONT color="green">142</FONT>            double fx = computeObjectiveValue(x);<a name="line.142"></a>
<FONT color="green">143</FONT>            if (!isMinim) {<a name="line.143"></a>
<FONT color="green">144</FONT>                fx = -fx;<a name="line.144"></a>
<FONT color="green">145</FONT>            }<a name="line.145"></a>
<FONT color="green">146</FONT>            double fv = fx;<a name="line.146"></a>
<FONT color="green">147</FONT>            double fw = fx;<a name="line.147"></a>
<FONT color="green">148</FONT>    <a name="line.148"></a>
<FONT color="green">149</FONT>            UnivariatePointValuePair previous = null;<a name="line.149"></a>
<FONT color="green">150</FONT>            UnivariatePointValuePair current<a name="line.150"></a>
<FONT color="green">151</FONT>                = new UnivariatePointValuePair(x, isMinim ? fx : -fx);<a name="line.151"></a>
<FONT color="green">152</FONT>            // Best point encountered so far (which is the initial guess).<a name="line.152"></a>
<FONT color="green">153</FONT>            UnivariatePointValuePair best = current;<a name="line.153"></a>
<FONT color="green">154</FONT>    <a name="line.154"></a>
<FONT color="green">155</FONT>            int iter = 0;<a name="line.155"></a>
<FONT color="green">156</FONT>            while (true) {<a name="line.156"></a>
<FONT color="green">157</FONT>                final double m = 0.5 * (a + b);<a name="line.157"></a>
<FONT color="green">158</FONT>                final double tol1 = relativeThreshold * FastMath.abs(x) + absoluteThreshold;<a name="line.158"></a>
<FONT color="green">159</FONT>                final double tol2 = 2 * tol1;<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>                // Default stopping criterion.<a name="line.161"></a>
<FONT color="green">162</FONT>                final boolean stop = FastMath.abs(x - m) &lt;= tol2 - 0.5 * (b - a);<a name="line.162"></a>
<FONT color="green">163</FONT>                if (!stop) {<a name="line.163"></a>
<FONT color="green">164</FONT>                    double p = 0;<a name="line.164"></a>
<FONT color="green">165</FONT>                    double q = 0;<a name="line.165"></a>
<FONT color="green">166</FONT>                    double r = 0;<a name="line.166"></a>
<FONT color="green">167</FONT>                    double u = 0;<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>                    if (FastMath.abs(e) &gt; tol1) { // Fit parabola.<a name="line.169"></a>
<FONT color="green">170</FONT>                        r = (x - w) * (fx - fv);<a name="line.170"></a>
<FONT color="green">171</FONT>                        q = (x - v) * (fx - fw);<a name="line.171"></a>
<FONT color="green">172</FONT>                        p = (x - v) * q - (x - w) * r;<a name="line.172"></a>
<FONT color="green">173</FONT>                        q = 2 * (q - r);<a name="line.173"></a>
<FONT color="green">174</FONT>    <a name="line.174"></a>
<FONT color="green">175</FONT>                        if (q &gt; 0) {<a name="line.175"></a>
<FONT color="green">176</FONT>                            p = -p;<a name="line.176"></a>
<FONT color="green">177</FONT>                        } else {<a name="line.177"></a>
<FONT color="green">178</FONT>                            q = -q;<a name="line.178"></a>
<FONT color="green">179</FONT>                        }<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>                        r = e;<a name="line.181"></a>
<FONT color="green">182</FONT>                        e = d;<a name="line.182"></a>
<FONT color="green">183</FONT>    <a name="line.183"></a>
<FONT color="green">184</FONT>                        if (p &gt; q * (a - x) &amp;&amp;<a name="line.184"></a>
<FONT color="green">185</FONT>                            p &lt; q * (b - x) &amp;&amp;<a name="line.185"></a>
<FONT color="green">186</FONT>                            FastMath.abs(p) &lt; FastMath.abs(0.5 * q * r)) {<a name="line.186"></a>
<FONT color="green">187</FONT>                            // Parabolic interpolation step.<a name="line.187"></a>
<FONT color="green">188</FONT>                            d = p / q;<a name="line.188"></a>
<FONT color="green">189</FONT>                            u = x + d;<a name="line.189"></a>
<FONT color="green">190</FONT>    <a name="line.190"></a>
<FONT color="green">191</FONT>                            // f must not be evaluated too close to a or b.<a name="line.191"></a>
<FONT color="green">192</FONT>                            if (u - a &lt; tol2 || b - u &lt; tol2) {<a name="line.192"></a>
<FONT color="green">193</FONT>                                if (x &lt;= m) {<a name="line.193"></a>
<FONT color="green">194</FONT>                                    d = tol1;<a name="line.194"></a>
<FONT color="green">195</FONT>                                } else {<a name="line.195"></a>
<FONT color="green">196</FONT>                                    d = -tol1;<a name="line.196"></a>
<FONT color="green">197</FONT>                                }<a name="line.197"></a>
<FONT color="green">198</FONT>                            }<a name="line.198"></a>
<FONT color="green">199</FONT>                        } else {<a name="line.199"></a>
<FONT color="green">200</FONT>                            // Golden section step.<a name="line.200"></a>
<FONT color="green">201</FONT>                            if (x &lt; m) {<a name="line.201"></a>
<FONT color="green">202</FONT>                                e = b - x;<a name="line.202"></a>
<FONT color="green">203</FONT>                            } else {<a name="line.203"></a>
<FONT color="green">204</FONT>                                e = a - x;<a name="line.204"></a>
<FONT color="green">205</FONT>                            }<a name="line.205"></a>
<FONT color="green">206</FONT>                            d = GOLDEN_SECTION * e;<a name="line.206"></a>
<FONT color="green">207</FONT>                        }<a name="line.207"></a>
<FONT color="green">208</FONT>                    } else {<a name="line.208"></a>
<FONT color="green">209</FONT>                        // Golden section step.<a name="line.209"></a>
<FONT color="green">210</FONT>                        if (x &lt; m) {<a name="line.210"></a>
<FONT color="green">211</FONT>                            e = b - x;<a name="line.211"></a>
<FONT color="green">212</FONT>                        } else {<a name="line.212"></a>
<FONT color="green">213</FONT>                            e = a - x;<a name="line.213"></a>
<FONT color="green">214</FONT>                        }<a name="line.214"></a>
<FONT color="green">215</FONT>                        d = GOLDEN_SECTION * e;<a name="line.215"></a>
<FONT color="green">216</FONT>                    }<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>                    // Update by at least "tol1".<a name="line.218"></a>
<FONT color="green">219</FONT>                    if (FastMath.abs(d) &lt; tol1) {<a name="line.219"></a>
<FONT color="green">220</FONT>                        if (d &gt;= 0) {<a name="line.220"></a>
<FONT color="green">221</FONT>                            u = x + tol1;<a name="line.221"></a>
<FONT color="green">222</FONT>                        } else {<a name="line.222"></a>
<FONT color="green">223</FONT>                            u = x - tol1;<a name="line.223"></a>
<FONT color="green">224</FONT>                        }<a name="line.224"></a>
<FONT color="green">225</FONT>                    } else {<a name="line.225"></a>
<FONT color="green">226</FONT>                        u = x + d;<a name="line.226"></a>
<FONT color="green">227</FONT>                    }<a name="line.227"></a>
<FONT color="green">228</FONT>    <a name="line.228"></a>
<FONT color="green">229</FONT>                    double fu = computeObjectiveValue(u);<a name="line.229"></a>
<FONT color="green">230</FONT>                    if (!isMinim) {<a name="line.230"></a>
<FONT color="green">231</FONT>                        fu = -fu;<a name="line.231"></a>
<FONT color="green">232</FONT>                    }<a name="line.232"></a>
<FONT color="green">233</FONT>    <a name="line.233"></a>
<FONT color="green">234</FONT>                    // User-defined convergence checker.<a name="line.234"></a>
<FONT color="green">235</FONT>                    previous = current;<a name="line.235"></a>
<FONT color="green">236</FONT>                    current = new UnivariatePointValuePair(u, isMinim ? fu : -fu);<a name="line.236"></a>
<FONT color="green">237</FONT>                    best = best(best,<a name="line.237"></a>
<FONT color="green">238</FONT>                                best(previous,<a name="line.238"></a>
<FONT color="green">239</FONT>                                     current,<a name="line.239"></a>
<FONT color="green">240</FONT>                                     isMinim),<a name="line.240"></a>
<FONT color="green">241</FONT>                                isMinim);<a name="line.241"></a>
<FONT color="green">242</FONT>    <a name="line.242"></a>
<FONT color="green">243</FONT>                    if (checker != null) {<a name="line.243"></a>
<FONT color="green">244</FONT>                        if (checker.converged(iter, previous, current)) {<a name="line.244"></a>
<FONT color="green">245</FONT>                            return best;<a name="line.245"></a>
<FONT color="green">246</FONT>                        }<a name="line.246"></a>
<FONT color="green">247</FONT>                    }<a name="line.247"></a>
<FONT color="green">248</FONT>    <a name="line.248"></a>
<FONT color="green">249</FONT>                    // Update a, b, v, w and x.<a name="line.249"></a>
<FONT color="green">250</FONT>                    if (fu &lt;= fx) {<a name="line.250"></a>
<FONT color="green">251</FONT>                        if (u &lt; x) {<a name="line.251"></a>
<FONT color="green">252</FONT>                            b = x;<a name="line.252"></a>
<FONT color="green">253</FONT>                        } else {<a name="line.253"></a>
<FONT color="green">254</FONT>                            a = x;<a name="line.254"></a>
<FONT color="green">255</FONT>                        }<a name="line.255"></a>
<FONT color="green">256</FONT>                        v = w;<a name="line.256"></a>
<FONT color="green">257</FONT>                        fv = fw;<a name="line.257"></a>
<FONT color="green">258</FONT>                        w = x;<a name="line.258"></a>
<FONT color="green">259</FONT>                        fw = fx;<a name="line.259"></a>
<FONT color="green">260</FONT>                        x = u;<a name="line.260"></a>
<FONT color="green">261</FONT>                        fx = fu;<a name="line.261"></a>
<FONT color="green">262</FONT>                    } else {<a name="line.262"></a>
<FONT color="green">263</FONT>                        if (u &lt; x) {<a name="line.263"></a>
<FONT color="green">264</FONT>                            a = u;<a name="line.264"></a>
<FONT color="green">265</FONT>                        } else {<a name="line.265"></a>
<FONT color="green">266</FONT>                            b = u;<a name="line.266"></a>
<FONT color="green">267</FONT>                        }<a name="line.267"></a>
<FONT color="green">268</FONT>                        if (fu &lt;= fw ||<a name="line.268"></a>
<FONT color="green">269</FONT>                            Precision.equals(w, x)) {<a name="line.269"></a>
<FONT color="green">270</FONT>                            v = w;<a name="line.270"></a>
<FONT color="green">271</FONT>                            fv = fw;<a name="line.271"></a>
<FONT color="green">272</FONT>                            w = u;<a name="line.272"></a>
<FONT color="green">273</FONT>                            fw = fu;<a name="line.273"></a>
<FONT color="green">274</FONT>                        } else if (fu &lt;= fv ||<a name="line.274"></a>
<FONT color="green">275</FONT>                                   Precision.equals(v, x) ||<a name="line.275"></a>
<FONT color="green">276</FONT>                                   Precision.equals(v, w)) {<a name="line.276"></a>
<FONT color="green">277</FONT>                            v = u;<a name="line.277"></a>
<FONT color="green">278</FONT>                            fv = fu;<a name="line.278"></a>
<FONT color="green">279</FONT>                        }<a name="line.279"></a>
<FONT color="green">280</FONT>                    }<a name="line.280"></a>
<FONT color="green">281</FONT>                } else { // Default termination (Brent's criterion).<a name="line.281"></a>
<FONT color="green">282</FONT>                    return best(best,<a name="line.282"></a>
<FONT color="green">283</FONT>                                best(previous,<a name="line.283"></a>
<FONT color="green">284</FONT>                                     current,<a name="line.284"></a>
<FONT color="green">285</FONT>                                     isMinim),<a name="line.285"></a>
<FONT color="green">286</FONT>                                isMinim);<a name="line.286"></a>
<FONT color="green">287</FONT>                }<a name="line.287"></a>
<FONT color="green">288</FONT>                ++iter;<a name="line.288"></a>
<FONT color="green">289</FONT>            }<a name="line.289"></a>
<FONT color="green">290</FONT>        }<a name="line.290"></a>
<FONT color="green">291</FONT>    <a name="line.291"></a>
<FONT color="green">292</FONT>        /**<a name="line.292"></a>
<FONT color="green">293</FONT>         * Selects the best of two points.<a name="line.293"></a>
<FONT color="green">294</FONT>         *<a name="line.294"></a>
<FONT color="green">295</FONT>         * @param a Point and value.<a name="line.295"></a>
<FONT color="green">296</FONT>         * @param b Point and value.<a name="line.296"></a>
<FONT color="green">297</FONT>         * @param isMinim {@code true} if the selected point must be the one with<a name="line.297"></a>
<FONT color="green">298</FONT>         * the lowest value.<a name="line.298"></a>
<FONT color="green">299</FONT>         * @return the best point, or {@code null} if {@code a} and {@code b} are<a name="line.299"></a>
<FONT color="green">300</FONT>         * both {@code null}. When {@code a} and {@code b} have the same function<a name="line.300"></a>
<FONT color="green">301</FONT>         * value, {@code a} is returned.<a name="line.301"></a>
<FONT color="green">302</FONT>         */<a name="line.302"></a>
<FONT color="green">303</FONT>        private UnivariatePointValuePair best(UnivariatePointValuePair a,<a name="line.303"></a>
<FONT color="green">304</FONT>                                              UnivariatePointValuePair b,<a name="line.304"></a>
<FONT color="green">305</FONT>                                              boolean isMinim) {<a name="line.305"></a>
<FONT color="green">306</FONT>            if (a == null) {<a name="line.306"></a>
<FONT color="green">307</FONT>                return b;<a name="line.307"></a>
<FONT color="green">308</FONT>            }<a name="line.308"></a>
<FONT color="green">309</FONT>            if (b == null) {<a name="line.309"></a>
<FONT color="green">310</FONT>                return a;<a name="line.310"></a>
<FONT color="green">311</FONT>            }<a name="line.311"></a>
<FONT color="green">312</FONT>    <a name="line.312"></a>
<FONT color="green">313</FONT>            if (isMinim) {<a name="line.313"></a>
<FONT color="green">314</FONT>                return a.getValue() &lt;= b.getValue() ? a : b;<a name="line.314"></a>
<FONT color="green">315</FONT>            } else {<a name="line.315"></a>
<FONT color="green">316</FONT>                return a.getValue() &gt;= b.getValue() ? a : b;<a name="line.316"></a>
<FONT color="green">317</FONT>            }<a name="line.317"></a>
<FONT color="green">318</FONT>        }<a name="line.318"></a>
<FONT color="green">319</FONT>    }<a name="line.319"></a>




























































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